Introduction to Pipe Theory and certain Diophatine equation

04/24/2012 - 12:15pm
04/24/2012 - 1:10pm
Willie Wu (CGU)

A pipe consists of two components: a value v and a finite set R of positive integers. The pair (v, R) is called a pipe if v - r is a product of at least two integers in R for each r in R. Many pipes are related to each other, such as polynomial pipes and linear pipes of any order (the order of the set R). Some pipes can be induced from (seed) pipes of a lower order. Some pipes are sporadic, but become seed for others. If an even value v is not a sum of two distinct primes (assume Goldbach conjecture fails), then v is a value of a basic pipe (even value v and prime set R). There are only 6 basic pipes for value v less than 500,000,000. I will discuss some potential basic pipes of order 5 with huge values. For each principal pipe of order 2, it is a solution of Diophatine equation: x + y^a = y + x^b with condition b > a > 1. There are 8 known solutions to this equation, and I believe there is no more. Readers may download the documents related to this topic at

Millikan 208 (Pomona College)